Which of the following is equal to log_10(0.01)? (2019)

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Question: Which of the following is equal to log_10(0.01)? (2019)

Options:

Correct Answer: -2

Exam Year: 2019

Solution:

log_10(0.01) = log_10(10^-2) = -2.

Which of the following is equal to log_10(0.01)? (2019)

Which of the following is equal to log_10(0.01)? (2019)

Step 1: Understand that log_10(x) means 'to what power must 10 be raised to get x'.
Step 2: Identify the value we are taking the logarithm of, which is 0.01.
Step 3: Rewrite 0.01 as a power of 10. We know that 0.01 is the same as 10 raised to the power of -2 (because 10^-2 = 1/10^2 = 1/100 = 0.01).
Step 4: Substitute this back into the logarithm: log_10(0.01) becomes log_10(10^-2).
Step 5: Use the property of logarithms that states log_b(b^x) = x. Here, b is 10 and x is -2.
Step 6: Therefore, log_10(10^-2) equals -2.

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